Marco Gualtieri

CLE Moore Instructor
MIT Mathematics Department

Research

My research areas are differential geometry and mathematical physics.
More specifically, I have been developing the theory of generalized geometrical structures initiated by my doctoral supervisor, Nigel Hitchin.
Most recently, I have been working on D-branes in generalized complex manifolds and the relation to noncommutative geometry, as well as further possible generalizations of classical geometries. So far, my collaborators are Gil R. Cavalcanti, Henrique Bursztyn, Vestislav Apostolov, and Tadashi Tokieda.

Here's a list of my available papers. There are several in the pipeline, so stay tuned:

  1. (new) Branes on Poisson varieties, using the theory of Poisson modules to construct examples of bi-Hermitian metrics on Poisson varieties.
  2. Generalized complex geometry, an article based on the thesis, significantly condensed (no generalized Kahler) and with several new ideas. Prepared while teaching the topics course below.
  3. Generalized complex geometry, my 2004 doctoral thesis. Develops the basic structure theory of generalized complex geometry as well as generalized Kaehler geometry
  4. Generalized complex structures on nilmanifolds, (J. Symp. Geom.) with Gil Cavalcanti. Some of the first nontrivial examples of generalized complex structures.
  5. Generalized geometry and the Hodge decomposition, proves a Hodge decomposition for generalized Kaehler structures.
  6. A surgery for generalized complex structures on 4-manifolds, (J. Diff. Geom.) with Gil Cavalcanti. Presents the first generalized complex 4-manifold which is neither symplectic nor complex.
  7. Reduction of Courant algebroids and generalized complex structures, with Henrique Bursztyn and Gil Cavalcanti. Develops a theory of reduction for Courant algebroids and related geometrical structures.
  8. Generalized Kaehler manifolds with split tangent bundle, with Vestislav Apostolov. Completes the classification of generalized Kaehler 4-manifolds.
  9. Golfer's Dilemma, (Am. J. Physics) with Tadashi Tokieda et al. Explains why the golf ball sometimes emerges from the hole.

Teaching

Schedule